Say I have two variables a and b and I know the full 2x2 covariance between them. Is there a Julia package to conveniently propagate Gaussian uncertainy through arbitrary functions of them in the same way that Measurements.jl works for single variables? Like I want: (a,b) = multivariate_measurement…

Maybe MonteCarloMeasurements.jl? [image] GitHub - baggepinnen/MonteCarloMeasurements.jl: Propagation of distributions... Propagation of distributions by Monte-Carlo sampling: Real number types with uncertainty represented by samples. - GitHub - baggepinnen/MonteCarloMeasurements.jl: Pro…

That was fast :laughing: :pray: julia> a, b = Particles(10000, MvNormal([10,12], [1 0.5; 0.5 1])) 2-element Vector{Particles{Float64, 10000}}: 10.0 ± 1.0 12.0 ± 1.0 julia> b^2 / a 14.4971 ± 2.11 Particles{Float64, 10000}

Beware though, it’s particle-based and not formula-based (at least I think so)

Will keep in mind, I think I’m in an ok regime though. I guess I would be interested still if there’s some AD-like formula-based thing.

If you ever see something like that, let me know. If not, I’d be interested in coding it, in case you wanna help?

Not exactly what you are asking for, but the Reachability Analysis community has some tools for “imprecise probabilities” that may be of value. They are guaranteed to bound the probabilities, however in some cases the over approximation can be too conservative to be useful. [image] GitHub …

You are right, MCM.jl is particle-based, the constructor is even called Particles :slight_smile: Since you are asking about AD-based solutions, I’ll note that you get exact propagation of multivariate normal distributions through linear functions using the unscented transform . These situations are …

[image] marius311: Say I have two variables a and b and I know the full 2x2 covariance between them. Is there a Julia package to conveniently propagate Gaussian uncertainy through arbitrary functions of them Fyi, the package Covar.jl might be of interest.

Does Julia have anything like Measurements.jl for multivariate error propagation?

General Usage

gdalle September 15, 2023, 6:19am 2

Maybe MonteCarloMeasurements.jl?

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Does Julia have anything like Measurements.jl for multivariate error propagation?

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